Math. Model. Nat. Phenom.
Volume 3, Number 1, 2008Interfacial phenomena in fluids
|Page(s)||75 - 97|
|Published online||17 July 2008|
The Effect of Crystal-Melt Surface Energy on the Stability of Ultra-Thin Melt Films
Andrews Space Inc., Seattle, WA, 98104, USA
2 Department of Materials Science and Engineering, University of Washington, Seattle, WA, 98195, USA
Corresponding author: email@example.com
The stability and evolution of very thin, single component, metallic-melt films is studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the film. Linear analysis reveals that there is a maximum applied far-field temperature in the gas, beyond which there is no film instability. Instabilities observed in the absence of CM surface energy are oscillatory for all marginally stable states. The effect of the CM surface energy is to expand the parameter range over which a film is unstable. The new range of instabilities are of longer wavelength and are stationary, compared to the range found in the absence of CM surface energy. Numerical analysis illustrates how perturbations grow to rupture by standing waves. With CM surface energy, an initially longer (stationary) wavelength perturbation has a relatively slow growth rate, but it can trigger the appearance of much faster growing shorter wavelength (oscillatory) instabilities, leading to an accelerated film rupture process.
Mathematics Subject Classification: 76D08 / 76E17 / 76E30 / 80A22
Key words: phase change / lubrication theory / interface instability / nonlinear / latent heat / crystal / van der Waals / long wavelength
© EDP Sciences, 2008
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